Epstein Secrets

hrough Newton's discovery of the laws of motion, through the experimental and theoretical investigations of the nature of electromagnetism, through Einstein's unification of space and time, through the discoveries of the nucleus, quantum mechanics, protons, neutrons, and the discovery of the weak and st

romagnetic wave whose speed could be calculated from first principles, and lo and behold, the prediction was equal to the mea- sured speed of light. Einstein's unification of space and time predicted that clocks would slow for moving observers, and lo and behold, they do, and in just the way he predicted

Strong Interactions." Sakurai took the 2P_GrealestSleryEverTold_AC.indd 192 12/16116 3:06 PIA EFTA00286114 Living inside a Superconductor 193 Yang-Mills suggestion seriously and tried to explore precisely which photonlike particles might convey a strong force between protons and neutrons and the oth

ited to try to make sense of the otherwise complex inter- actions between nucleons and other particles. In response to this notion that some kind of Yang-Mills symmetry might be behind the strong interaction, Murray Gell-Mann developed an elegant symmetry scheme he labeled in a Zen-like fashion the Eight-

quantum craziness of reality was taken by an unlikely explorer, Paul Adrien Maurice Dirac. In one sense, Dirac was the perfect man for the job. As Einstein is re- puted to have later said of him, "This balancing on the dizzying path between genius and madness is awful! When I think of Dirac, an old jok

low you to move pieces across the board to distant locations. In short, a gauge symmetry such as that in electromagnetism, or in the more esoteric Yang-Mills proposal, only works if the new fields re- quired by the symmetry are massless. Amid all the mathematical com- plexity, this one fact is inviolate.

particular mathematical prop- erty of matrices that makes multiplying them different from multiplying numbers—or, in deference to Yang and Mills, a Yang-Mills symmetry. Yang and Mills's article appears at first glance to be an abstract—or purely speculative—mathematical exploration of the implications of

§0,(x) where 122 = 1 + 2e4)t./All, (2) is the conformal factor and Alp is the reduced Planck mass. By doing so, one passes from the Jordan to the Einstein frame. The scalar potential in the new frame becomes V (h) Am 4 (1 + ) 2 (3) where we have written et = h2/ 2. At large field values, h > Mp/

ulations typically involve spurious gauge dependence that cancels when physical ob- servable are calculated. For example, in a spontaneously broken Yang-Mills theory one may work in the renormaliz- able class of gauges (RE) upon augmenting the Lagrangian with a gauge fixing term Cil = —GaG a /2 where G a

li,„(s) where D2 = 1 + 2e(}141/4/1, (2) is the conformal factor and My is the reduced Planck mass. By doing so. one passes from the Jordan to the Einstein frame. The scalar potential in the new frame becomes V(h) 2 (3) 4 (1 + where we have written 4.147, = h2/ 2. At large field values. h > ii/p/V

ulations typically involve spurious gauge dependence that cancels when physical ob- servable arc calculated. For example, in a spontaneously broken Yang-Mills theory one may work in the renormaliz- able class of gauges (RO upon augmenting the Lagrangian with a gauge fixing term Cgi = —G°Ga/2 where = (1/